We've been up to Atherton and also to Shadow Mountain campgrounds. As stated, Atherton charges a bit more, but is more organized, with a vaulted toilet and fishing and peace and quiet. There appear to be some pull out places along the way to Atherton after you climb up off the flats a bit.
Shadow Mountain can be totally empty or there can be a half dozen tenters. It is sandy no one cuts what grass and weeds there are, but it sits in a stand of cottonwoods and has a terrific view of the Tetons.
You could alternate your stay between these places and the NP gros ventre campground for your water and dump station.
There are some more spots up on the north end out of Flagg Ranch on Grassy Lake Road..right along the river, very scenic, but each spot has only two or three sites..and a vaulted toilet.
Good luck and enjoy your stay.
TexasShadow
Holiday Rambler Endeavor LE/ 3126B Cat
Sometimes BMW K75 on Rear Carrier
Jeep Grand Cherokee or 2016 Ford XLT 4x4 super cab with 8 ft bed
M&G aux brake system
854 Watts of Solar Power
Always remember you're unique, just like everyone else.